Global linear stability of the bubble rising in the presence of a soluble surfactant

Abstract

We study the stability of the bubble rising in the presence of a soluble surfactant numerically and experimentally. For the surfactant concentration considered, the Marangoni stress almost immobilizes the interface. However, the non-zero surface velocity is crucial to understanding the surfactant behavior. The global linear stability analysis predicts the transition to an oblique path above the threshold of the Galilei number (the bubble radius). This transition is followed by the coexistence of stationary and oscillatory instabilities as the Galieli number increases. These predictions agree with the experimental observations without any fitting parameters. The bubble deformation, hydrostatic pressure variation, and perturbed viscous stress are evaluated. The velocity field perturbation causes a destabilizing vortex in the rear of the bubble. The perturbed viscous stress produces a torque opposing this vortex. The torque significantly decreases above the critical Galilei number, which may constitute the origin of instability. The linear stability analysis and the experiments were conducted for Surfynol, which can be regarded as a fast surfactant. Our experiments show the considerable differences between the rising of bubbles in the presence of this surfactant and a regular one.